Block-matching and 3D filtering

Grouping Image fragments are grouped together based on similarity, but unlike standard k-means clustering and such cluster analysis methods, the image fragments are not necessarily disjoint. This block-matching algorithm is less computationally demanding and is useful later on in the aggregation step. Fragments do however have the same size. A fragment is grouped if its dissimilarity with a reference fragment falls below a specified threshold. This grouping technique is called block-matching, it is typically used to group similar groups across different frames of a digital video, BM3D on the other hand may group macroblocks within a single frame. All image fragments in a group are then stacked to form 3D cylinder-like shapes. Collaborative filtering Filtering is done on every fragments group. A d+1 dimensional linear transform is applied, followed by a transform-domain shrinkage such as Wiener filtering, then the linear transform is inverted to reproduce all (filtered) fragments. Aggregation The image is transformed back into its two-dimensional form. All overlapping image fragments are weight-averaged to ensure that they are filtered for noise yet retain their distinct signal. == Extensions ==

Color images RGB images can be processed much like grayscale ones. A luminance-chrominance transformation should be applied to the RGB image. The grouping is then completed on the luminance channel which contains most of the useful information and a higher SNR. This approach works because the noise in the chrominance channels is strongly correlated to that of the luminance channel, and it saves approximately one-third of the computing time because grouping takes up approximately half of the required computing time. Deblurring The BM3D algorithm has been extended (IDD-BM3D) to perform decoupled deblurring and denoising using the Nash equilibrium balance of the two objective functions. Convolutional neural network An approach that integrates a convolutional neural network has been proposed and shows better results (albeit with a slower runtime). MATLAB code has been released for research purpose. == Implementations ==

• Reference implementation in MATLAB and Python released under an open-source proprietary license: BM3D • Well documented C-based implementation released under the GPLv3: bm3d • CUDA and C++ based implementation released under the GPLv3: bm3d-gpu == References ==